conv.py

#   Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

# TODO: define classes of convolutional neural network

__all__ = [
    'Conv2d',
    'Conv3d',
    'ConvTranspose2d',
    'ConvTranspose3d',
    #       'TreeConv',
    #       'Conv1D'
]

import numpy as np

from ...fluid.dygraph import layers
from ...fluid.initializer import Normal
from .. import functional as F
from ...fluid.layers import utils
from ..functional.conv import _update_padding_nd


def _get_default_param_initializer(num_channels, filter_size):
    filter_elem_num = num_channels * np.prod(filter_size)
    std = (2.0 / filter_elem_num)**0.5
    return Normal(0.0, std, 0)


def _reverse_repeat_list(t, n):
    """Reverse the order of `t` and repeat each element for `n` times.

    This can be used to translate padding arg used by Conv and Pooling modules
    to the ones used by `F.pad`.
    """
    return list(x for x in reversed(t) for _ in range(n))


class _ConvNd(layers.Layer):
    def __init__(self,
                 in_channels,
                 out_channels,
                 kernel_size,
                 transposed,
                 dims,
                 stride=1,
                 padding=0,
                 padding_mode='zeros',
                 output_padding=0,
                 dilation=1,
                 groups=1,
                 weight_attr=None,
                 bias_attr=None,
                 data_format="NCHW"):
        super(_ConvNd, self).__init__()
        assert weight_attr is not False, "weight_attr should not be False in Conv."
        self._param_attr = weight_attr
        self._bias_attr = bias_attr
        self._groups = groups
        self._in_channels = in_channels
        self._out_channels = out_channels
        self._data_format = data_format

        valid_padding_modes = {'zeros', 'reflect', 'replicate', 'circular'}
        if padding_mode not in valid_padding_modes:
            raise ValueError(
                "padding_mode must be one of {}, but got padding_mode='{}'".
                format(valid_padding_modes, padding_mode))

        if padding_mode in {'reflect', 'replicate', 'circular'
                            } and not isinstance(padding, np.int):
            raise TypeError(
                "when padding_mode in ['reflect', 'replicate', 'circular'], type of padding must be int"
            )

        self._stride = utils.convert_to_list(stride, dims, 'stride')
        self._dilation = utils.convert_to_list(dilation, dims, 'dilation')
        self._kernel_size = utils.convert_to_list(kernel_size, dims,
                                                  'kernel_size')
        self._padding = padding
        self._padding_mode = padding_mode
        self.output_padding = output_padding

        if transposed:
            filter_shape = [self._in_channels, out_channels // groups
                            ] + self._kernel_size
        else:
            if in_channels % groups != 0:
                raise ValueError("in_channels must be divisible by groups.")

            if padding_mode in {'reflect', 'replicate', 'circular'}:
                _paired_padding = utils.convert_to_list(padding, 2, 'padding')
                self._reversed_padding_repeated_twice = _reverse_repeat_list(
                    _paired_padding, 2)

            filter_shape = [out_channels, in_channels // groups
                            ] + self._kernel_size

        self.weight = self.create_parameter(
            shape=filter_shape, attr=self._param_attr)
        self.bias = self.create_parameter(
            attr=self._bias_attr, shape=[self._out_channels], is_bias=True)


class Conv2d(_ConvNd):
    """

    This interface is used to construct a callable object of the ``Conv2d`` class.
    For more details, refer to code examples.
    The convolution2D layer calculates the output based on the input, filter
    and strides, paddings, dilations, groups parameters. Input and
    Output are in NCHW format, where N is batch size, C is the number of
    the feature map, H is the height of the feature map, and W is the width of the feature map.
    Filter's shape is [MCHW] , where M is the number of output feature map,
    C is the number of input feature map, H is the height of the filter,
    and W is the width of the filter. If the groups is greater than 1,
    C will equal the number of input feature map divided by the groups.
    Please refer to UFLDL's `convolution
    <http://ufldl.stanford.edu/tutorial/supervised/FeatureExtractionUsingConvolution/>`_
    for more details.
    If bias attribution and activation type are provided, bias is added to the
    output of the convolution, and the corresponding activation function is
    applied to the final result.

    For each input :math:`X`, the equation is:

    .. math::

        Out = \\sigma (W \\ast X + b)

    Where:

    * :math:`X`: Input value, a ``Tensor`` with NCHW format.
    * :math:`W`: Filter value, a ``Tensor`` with shape [MCHW] .
    * :math:`\\ast`: Convolution operation.
    * :math:`b`: Bias value, a 2-D ``Tensor`` with shape [M, 1].
    * :math:`\\sigma`: Activation function.
    * :math:`Out`: Output value, the shape of :math:`Out` and :math:`X` may be different.

    Parameters:
        in_channels(int): The number of channels in the input image.
        out_channels(int): The number of channels produced by convolution.
        kernel_size (int|list|tuple): The size of convolution kernel.
        stride (int|list|tuple, optional): The stride size. If stride is a tuple, it must
            contain two integers, (stride_H, stride_W). Otherwise, the
            stride_H = stride_W = stride. Default: 1.
        padding(int|str|tuple|list, optional): The padding size. Padding coule be in one of the following forms.
            1. a string in ['valid', 'same'].
            2. an int, which means each spartial dimension(depth, height, width) is zero paded by size of `padding`on both sides 
            3. a list[int] or tuple[int] whose length is the number of spartial dimensions, which contains the amount of padding on each side for each spartial dimension. It has the form [pad_d1, pad_d2, ...].
            4. a list[int] or tuple[int] whose length is 2 * number of spartial dimensions. It has the form  [pad_before, pad_after, pad_before, pad_after, ...] for all spartial dimensions.
            5. a list or tuple of pairs of ints. It has the form [[pad_before, pad_after], [pad_before, pad_after], ...]. Note that, the batch dimension and channel dimension are also included. Each pair of integers correspond to the amount of padding for a dimension of the input. Padding in batch dimension and channel dimension should be [0, 0] or (0, 0).
            The default value is 0.
        padding_mode (str, optional): ``'zeros'``, ``'reflect'``, ``'replicate'`` or ``'circular'``. Default: ``'zeros'`` .
        dilation (int|list|tuple, optional): The dilation size. If dilation is a tuple, it must
            contain two integers, (dilation_H, dilation_W). Otherwise, the
            dilation_H = dilation_W = dilation. Default: 1.
        groups (int, optional): The groups number of the Conv2d Layer. According to grouped
            convolution in Alex Krizhevsky's Deep CNN paper: when group=2,
            the first half of the filters is only connected to the first half
            of the input channels, while the second half of the filters is only
            connected to the second half of the input channels. Default: 1.
        weight_attr (ParamAttr, optional): The parameter attribute for learnable weights(Parameter)
            of conv2d. If it is set to None or one attribute of ParamAttr, conv2d
            will create ParamAttr as param_attr. If the Initializer of the param_attr
            is not set, the parameter is initialized with :math:`Normal(0.0, std)`,
            and the :math:`std` is :math:`(\\frac{2.0 }{filter\_elem\_num})^{0.5}`. Default: None.
        bias_attr (ParamAttr|bool, optional): The attribute for the bias of conv2d.
            If it is set to False, no bias will be added to the output units.
            If it is set to None or one attribute of ParamAttr, conv2d
            will create ParamAttr as bias_attr. If the Initializer of the bias_attr
            is not set, the bias is initialized zero. Default: None.
        data_format (str, optional): Data format that specifies the layout of input.
            It can be "NCHW" or "NHWC". Default: "NCHW".

    Attribute:
        **weight** (Parameter): the learnable weights of filter of this layer.

        **bias** (Parameter or None): the learnable bias of this layer.

    Shape:

        - x: :math:`(N, C_{in}, H_{in}, W_{in})`

        - output: :math:`(N, C_{out}, H_{out}, W_{out})`

        Where

        .. math::

           H_{out}&= \\frac{(H_{in} + 2 * paddings[0] - (dilations[0] * (kernel_size[0] - 1) + 1))}{strides[0]} + 1 \\\\
           W_{out}&= \\frac{(W_{in} + 2 * paddings[1] - (dilations[1] * (kernel_size[1] - 1) + 1))}{strides[1]} + 1

    Examples:
        .. code-block:: python

          import numpy as np
    
          import paddle
          import paddle.nn as nn

          x = np.random.uniform(-1, 1, (2, 4, 8, 8)).astype('float32')
          
          paddle.disable_static()

          x_var = paddle.to_tensor(x)
          conv = nn.Conv2d(4, 6, (3, 3))
          y_var = conv(x_var)
          y_np = y_var.numpy()
          print(y_np.shape)
          
          # (2, 6, 6, 6)
    """

    def __init__(self,
                 in_channels,
                 out_channels,
                 kernel_size,
                 stride=1,
                 padding=0,
                 dilation=1,
                 groups=1,
                 padding_mode='zeros',
                 weight_attr=None,
                 bias_attr=None,
                 data_format="NCHW"):
        super(Conv2d, self).__init__(
            in_channels,
            out_channels,
            kernel_size,
            False,
            2,
            stride=stride,
            padding=padding,
            padding_mode=padding_mode,
            dilation=dilation,
            groups=groups,
            weight_attr=weight_attr,
            bias_attr=bias_attr,
            data_format=data_format)

    def forward(self, x):
        if self._padding_mode != 'zeros':
            x = F.pad(x,
                      self._reversed_padding_repeated_twice,
                      mode=self._padding_mode,
                      data_format=self._data_format)
            return F.conv2d(
                x,
                self.weight,
                bias=self.bias,
                stride=self._stride,
                dilation=self._dilation,
                groups=self._groups,
                data_format=self._data_format)

        out = F.conv2d(
            x,
            self.weight,
            bias=self.bias,
            padding=self._padding,
            stride=self._stride,
            dilation=self._dilation,
            groups=self._groups,
            data_format=self._data_format)
        return out


class ConvTranspose2d(_ConvNd):
    """
    This interface is used to construct a callable object of the ``ConvTranspose2d`` class.
    For more details, refer to code examples.
    The convolution2D transpose layer calculates the output based on the input,
    filter, and dilations, strides, paddings. Input and output
    are in NCHW format. Where N is batch size, C is the number of feature map,
    H is the height of the feature map, and W is the width of the feature map.
    Filter's shape is [MCHW] , where M is the number of input feature map,
    C is the number of output feature map, H is the height of the filter,
    and W is the width of the filter. If the groups is greater than 1,
    C will equal the number of input feature map divided by the groups.
    If bias attribution and activation type are provided, bias is added to
    the output of the convolution, and the corresponding activation function
    is applied to the final result.
    The details of convolution transpose layer, please refer to the following explanation and references
    `conv2dtranspose <http://www.matthewzeiler.com/wp-content/uploads/2017/07/cvpr2010.pdf>`_ .

    For each input :math:`X`, the equation is:

    .. math::

        Out = \sigma (W \\ast X + b)

    Where:

    * :math:`X`: Input value, a ``Tensor`` with NCHW format.
    * :math:`W`: Filter value, a ``Tensor`` with shape [MCHW] .
    * :math:`\\ast`: Convolution operation.
    * :math:`b`: Bias value, a 2-D ``Tensor`` with shape [M, 1].
    * :math:`\\sigma`: Activation function.
    * :math:`Out`: Output value, the shape of :math:`Out` and :math:`X` may be different.

    Example:

        - Input:

          Input shape: :math:`(N, C_{in}, H_{in}, W_{in})`

          Filter shape: :math:`(C_{in}, C_{out}, H_f, W_f)`

        - Output:

          Output shape: :math:`(N, C_{out}, H_{out}, W_{out})`

        Where

        .. math::

           H^\prime_{out} &= (H_{in} - 1) * strides[0] - 2 * paddings[0] + dilations[0] * (H_f - 1) + 1 \\\\
           W^\prime_{out} &= (W_{in} - 1) * strides[1] - 2 * paddings[1] + dilations[1] * (W_f - 1) + 1 \\\\
           H_{out} &\in [ H^\prime_{out}, H^\prime_{out} + strides[0] ) \\\\
           W_{out} &\in [ W^\prime_{out}, W^\prime_{out} + strides[1] )

    Parameters:
        in_channels(int): The number of channels in the input image.
        out_channels(int): The number of channels produced by the convolution.
        kernel_size(int|list|uple): The kernel size. If kernel_size is a tuple,
            it must contain two integers, (kernel_size_H, kernel_size_W).
            Otherwise, the kernel will be a square.
        output_padding(int|list|tuple, optional): Additional size added to one side
            of each dimension in the output shape. Default: 0.
        padding(int|str|tuple|list, optional): The padding size. Padding coule be in one of the following forms.
            1. a string in ['valid', 'same'].
            2. an int, which means each spartial dimension(depth, height, width) is zero paded by size of `padding` on both sides 
            3. a list[int] or tuple[int] whose length is the number of spartial dimensions, which contains the amount of padding on each side for each spartial dimension. It has the form [pad_d1, pad_d2, ...].
            4. a list[int] or tuple[int] whose length is 2 * number of spartial dimensions. It has the form  [pad_before, pad_after, pad_before, pad_after, ...] for all spartial dimensions.
            5. a list or tuple of pairs of ints. It has the form [[pad_before, pad_after], [pad_before, pad_after], ...]. Note that, the batch dimension and channel dimension are also included. Each pair of integers correspond to the amount of padding for a dimension of the input. Padding in batch dimension and channel dimension should be [0, 0] or (0, 0).
            The default value is 0.
        stride(int|list|tuple, optional): The stride size. If stride is a tuple, it must
            contain two integers, (stride_H, stride_W). Otherwise, the
            stride_H = stride_W = stride. Default: 1.
        dilation(int|list|tuple, optional): The dilation size. If dilation is a tuple, it must
            contain two integers, (dilation_H, dilation_W). Otherwise, the
            dilation_H = dilation_W = dilation. Default: 1.
        groups(int, optional): The groups number of the Conv2d transpose layer. Inspired by
            grouped convolution in Alex Krizhevsky's Deep CNN paper, in which
            when group=2, the first half of the filters is only connected to the
            first half of the input channels, while the second half of the
            filters is only connected to the second half of the input channels.
            Default: 1.
        weight_attr (ParamAttr, optional): The parameter attribute for learnable weights(Parameter)
            of conv2d_transpose. If it is set to None or one attribute of ParamAttr, conv2d_transpose
            will create ParamAttr as param_attr. If the Initializer of the param_attr
            is not set, the parameter is initialized with Xavier. Default: None.
        bias_attr (ParamAttr|bool, optional): The attribute for the bias of conv2d_transpose.
            If it is set to False, no bias will be added to the output units.
            If it is set to None or one attribute of ParamAttr, conv2d_transpose
            will create ParamAttr as bias_attr. If the Initializer of the bias_attr
            is not set, the bias is initialized zero. Default: None.
        data_format (str, optional): Data format that specifies the layout of input.
            It can be "NCHW" or "NHWC". Default: "NCHW".

    Attribute:
        **weight** (Parameter): the learnable weights of filters of this layer.

        **bias** (Parameter or None): the learnable bias of this layer.

    Shape:
        - x: :math:`(N, C_{in}, H_{in}, W_{in})`

        - output: :math:`(N, C_{out}, H_{out}, W_{out})`

        Where

        .. math::

           H^\prime_{out} &= (H_{in} - 1) * strides[0] - 2 * paddings[0] + dilations[0] * (kernel_size[0] - 1) + 1 \\\\
           W^\prime_{out} &= (W_{in} - 1) * strides[1] - 2 * paddings[1] + dilations[1] * (kernel_size[1] - 1) + 1 \\\\

    Examples:
       .. code-block:: python

          import numpy as np
          import paddle
          import paddle.nn as nn

          x = np.random.uniform(-1, 1, (2, 4, 8, 8)).astype('float32')

          paddle.disable_static()

          x_var = paddle.to_tensor(x)
          conv = nn.ConvTranspose2d(4, 6, (3, 3))
          y_var = conv(x_var)
          y_np = y_var.numpy()
          print(y_np.shape)
          
          # (2, 6, 10, 10)
    """

    def __init__(self,
                 in_channels,
                 out_channels,
                 kernel_size,
                 stride=1,
                 padding=0,
                 output_padding=0,
                 dilation=1,
                 groups=1,
                 weight_attr=None,
                 bias_attr=None,
                 data_format="NCHW"):
        super(ConvTranspose2d, self).__init__(
            in_channels,
            out_channels,
            kernel_size,
            True,
            2,
            stride=stride,
            padding=padding,
            dilation=dilation,
            output_padding=output_padding,
            groups=groups,
            weight_attr=weight_attr,
            bias_attr=bias_attr,
            data_format=data_format)

    def forward(self, x, output_size=None):
        if output_size is None:
            output_padding = self.output_padding
        else:
            output_padding = 0

        out = F.conv_transpose2d(
            x,
            self.weight,
            bias=self.bias,
            padding=self._padding,
            output_padding=output_padding,
            stride=self._stride,
            dilation=self._dilation,
            groups=self._groups,
            output_size=output_size,
            data_format=self._data_format)
        return out


class Conv3d(_ConvNd):
    """

    **Convlution3d Layer**

    The convolution3d layer calculates the output based on the input, filter
    and strides, paddings, dilations, groups parameters. Input(Input) and
    Output(Output) are multidimensional tensors with a shape of 
    :math:`[N, C, D, H, W]` . Where N is batch size, C is the number of
    channels, D is the depth of the feature, H is the height of the feature,
    and W is the width of the feature. Convlution3D is similar with Convlution2D
    but adds one dimension(depth). If bias attribution and activation type are
    provided, bias is added to the output of the convolution, and the
    corresponding activation function is applied to the final result.

    For each input :math:`X`, the equation is:

    .. math::

        Out = \sigma (W \\ast X + b)

    In the above equation:

    * :math:`X`: Input value, a tensor with NCDHW or NDHWC format.
    * :math:`W`: Filter value, a tensor with MCDHW format.
    * :math:`\\ast`: Convolution operation.
    * :math:`b`: Bias value, a 2-D tensor with shape [M, 1].
    * :math:`\\sigma`: Activation function.
    * :math:`Out`: Output value, the shape of :math:`Out` and :math:`X` may be different.

    Parameters:
        in_channels(int): The number of input channels in the input image.
        out_channels(int): The number of output channels produced by the convolution.
        kernel_size (int|list|tuple, optional): The size of the convolving kernel.
        stride (int|list|tuple, optional): The stride size. If stride is a tuple, it must
            contain three integers, (stride_D, stride_H, stride_W). Otherwise, the
            stride_D = stride_H = stride_W = stride. The default value is 1.
        padding (int|str|tuple|list, optional): The padding size. Padding coule be in one of the following forms.
            1. a string in ['valid', 'same'].
            2. an int, which means each spartial dimension(depth, height, width) is zero paded by size of `padding` 
            3. a list[int] or tuple[int] whose length is the number of spartial dimensions, which contains the amount of padding on each side for each spartial dimension. It has the form [pad_d1, pad_d2, ...].
            4. a list[int] or tuple[int] whose length is 2 * number of spartial dimensions. It has the form  [pad_before, pad_after, pad_before, pad_after, ...] for all spartial dimensions.
            5. a list or tuple of pairs of ints. It has the form [[pad_before, pad_after], [pad_before, pad_after], ...]. Note that, the batch dimension and channel dimension are also included. Each pair of integers correspond to the amount of padding for a dimension of the input. Padding in batch dimension and channel dimension should be [0, 0] or (0, 0).
            The default value is 0.
        dilation (int|list|tuple, optional): The dilation size. If dilation is a tuple, it must
            contain three integers, (dilation_D, dilation_H, dilation_W). Otherwise, the
            dilation_D = dilation_H = dilation_W = dilation. The default value is 1.
        groups (int, optional): The groups number of the Conv3d Layer. According to grouped
            convolution in Alex Krizhevsky's Deep CNN paper: when group=2,
            the first half of the filters is only connected to the first half
            of the input channels, while the second half of the filters is only
            connected to the second half of the input channels. The default value is 1.
        padding_mode (str, optional): ``'zeros'``, ``'reflect'``, ``'replicate'`` or ``'circular'``. Default: ``'zeros'``.
        weight_attr (ParamAttr, optional): The parameter attribute for learnable parameters/weights
            of conv3d. If it is set to None or one attribute of ParamAttr, conv3d
            will create ParamAttr as param_attr. If it is set to None, the parameter
            is initialized with :math:`Normal(0.0, std)`, and the :math:`std` is
            :math:`(\\frac{2.0 }{filter\_elem\_num})^{0.5}`. The default value is None.
        bias_attr (ParamAttr|bool, optional): The parameter attribute for the bias of conv3d.
            If it is set to False, no bias will be added to the output units.
            If it is set to None or one attribute of ParamAttr, conv3d
            will create ParamAttr as bias_attr. If the Initializer of the bias_attr
            is not set, the bias is initialized zero. The default value is None.
        data_format (str, optional): Data format that specifies the layout of input.
            It can be "NCDHW" or "NDHWC". Default: "NCDHW".

    Attribute:
        **weight** (Parameter): the learnable weights of filters of this layer.

        **bias** (Parameter): the learnable bias of this layer.

    Shape:

        - x: :math:`(N, C_{in}, D_{in}, H_{in}, W_{in})`

        - output: :math:`(N, C_{out}, D_{out}, H_{out}, W_{out})`

        Where

        .. math::

           D_{out}&= \\frac{(D_{in} + 2 * paddings[0] - (dilations[0] * (D_f - 1) + 1))}{strides[0]} + 1 \\\\
           H_{out}&= \\frac{(H_{in} + 2 * paddings[1] - (dilations[1] * (H_f - 1) + 1))}{strides[1]} + 1 \\\\
           W_{out}&= \\frac{(W_{in} + 2 * paddings[2] - (dilations[2] * (W_f - 1) + 1))}{strides[2]} + 1

    Raises:
        ValueError: If the shapes of input, filter_size, stride, padding and
                    groups mismatch.

    Examples:
        .. code-block:: python

          import numpy as np
          
          import paddle
          import paddle.nn as nn

          x = np.random.uniform(-1, 1, (2, 4, 8, 8, 8)).astype('float32')
          
          paddle.disable_static()

          x_var = dg.to_variable(x)
          conv = nn.Conv3d(4, 6, (3, 3, 3))
          y_var = conv(x_var)
          y_np = y_var.numpy()
          print(y_np.shape)
          
          # (2, 6, 6, 6, 6)
    """

    def __init__(self,
                 in_channels,
                 out_channels,
                 kernel_size,
                 padding=0,
                 stride=1,
                 dilation=1,
                 groups=1,
                 padding_mode='zeros',
                 weight_attr=None,
                 bias_attr=None,
                 data_format="NCDHW"):
        super(Conv3d, self).__init__(
            in_channels,
            out_channels,
            kernel_size,
            False,
            3,
            stride=stride,
            padding=padding,
            padding_mode=padding_mode,
            dilation=dilation,
            groups=groups,
            weight_attr=weight_attr,
            bias_attr=bias_attr,
            data_format=data_format)

    def forward(self, x):
        if self._padding_mode != 'zeros':
            x = F.pad(x,
                      self._reversed_padding_repeated_twice,
                      mode=self._padding_mode,
                      data_format=self._data_format)
            return F.conv3d(
                x,
                self.weight,
                bias=self.bias,
                stride=self._stride,
                dilation=self._dilation,
                groups=self._groups,
                data_format=self._data_format)

        out = F.conv3d(
            x,
            self.weight,
            bias=self.bias,
            padding=self._padding,
            stride=self._stride,
            dilation=self._dilation,
            groups=self._groups,
            data_format=self._data_format)
        return out


class ConvTranspose3d(_ConvNd):
    """

    **Convlution3D transpose layer**

    The convolution3D transpose layer calculates the output based on the input,
    filter, and dilations, strides, paddings. Input(Input) and output(Output)
    are in NCDHW format. Where N is batch size, C is the number of channels,
    D is the depth of the feature, H is the height of the feature, and W
    is the width of the feature. Parameters(dilations, strides, paddings) are
    two elements. These two elements represent height and width, respectively.
    The details of convolution transpose layer, please refer to the following
    explanation and references `therein <http://www.matthewzeiler.com/wp-content/uploads/2017/07/cvpr2010.pdf>`_.
    If bias attribution and activation type are provided, bias is added to
    the output of the convolution, and the corresponding activation function
    is applied to the final result.

    For each input :math:`X`, the equation is:

    .. math::

        Out = \sigma (W \\ast X + b)

    In the above equation:

    * :math:`X`: Input value, a tensor with NCDHW format.
    * :math:`W`: Filter value, a tensor with MCDHW format.
    * :math:`\\ast`: Convolution operation.
    * :math:`b`: Bias value, a 2-D tensor with shape [M, 1].
    * :math:`\\sigma`: Activation function.
    * :math:`Out`: Output value, the shape of :math:`Out` and :math:`X` may be different.

    Example:

    **Note**:

          The conv_transpose3d can be seen as the backward of the conv3d. For conv3d, 
          when stride > 1, conv3d maps multiple input shape to the same output shape, 
          so for conv_transpose3d, when stride > 1, input shape maps multiple output shape.
          If output_size is None, :math:`H_{out} = H^\prime_{out}, :math:`H_{out} = \
          H^\prime_{out}, W_{out} = W^\prime_{out}`; else, the :math:`D_{out}` of the output 
          size must between :math:`D^\prime_{out}` and :math:`D^\prime_{out} + strides[0]`, 
          the :math:`H_{out}` of the output size must between :math:`H^\prime_{out}` 
          and :math:`H^\prime_{out} + strides[1]`, and the :math:`W_{out}` of the output size must 
          between :math:`W^\prime_{out}` and :math:`W^\prime_{out} + strides[2]`, 
          conv_transpose3d can compute the kernel size automatically.


    Parameters:
        in_channels(int): The number of channels in the input image.
        out_channels(int): The number of channels produced by the convolution.
        kernel_size(int|list|tuple): The kernel size. If kernel_size is a tuple,
            it must contain three integers, (kernel_size_D, kernel_size_H, kernel_size_W).
            Otherwise, the kernel will be a square.
        stride(int|list|tuple, optional): The stride size. It means the stride in transposed convolution. 
            If stride is a tuple, it must contain three integers, (stride_depth, stride_height, 
            stride_width). Otherwise, stride_depth = stride_height = stride_width = stride. 
            The default value is 1.
        padding(int|str|tuple|list, optional): The padding size. Padding coule be in one of the following forms.
            1. a string in ['valid', 'same'].
            2. an int, which means each spartial dimension(depth, height, width) is zero paded by size of `padding` 
            3. a list[int] or tuple[int] whose length is the number of spartial dimensions, which contains the amount of padding on each side for each spartial dimension. It has the form [pad_d1, pad_d2, ...].
            4. a list[int] or tuple[int] whose length is 2 * number of spartial dimensions. It has the form  [pad_before, pad_after, pad_before, pad_after, ...] for all spartial dimensions.
            5. a list or tuple of pairs of ints. It has the form [[pad_before, pad_after], [pad_before, pad_after], ...]. Note that, the batch dimension and channel dimension are also included. Each pair of integers correspond to the amount of padding for a dimension of the input. Padding in batch dimension and channel dimension should be [0, 0] or (0, 0).
            The default value is 0.
        output_padding(int|list|tuple, optional): Additional size added to one side
            of each dimension in the output shape. Default: 0.
        dilation(int|list|tuple, optional): The dilation size. If dilation is a tuple, it must
            contain three integers, (dilation_D, dilation_H, dilation_W). Otherwise, the
            dilation_D = dilation_H = dilation_W = dilation. The default value is 1.
        groups(int, optional): The groups number of the Conv3d transpose layer. Inspired by
            grouped convolution in Alex Krizhevsky's Deep CNN paper, in which
            when group=2, the first half of the filters is only connected to the
            first half of the input channels, while the second half of the
            filters is only connected to the second half of the input channels.
            The default value is 1.
        weight_attr (ParamAttr, optional): The parameter attribute for learnable parameters/weights
            of conv3d_transpose. If it is set to None or one attribute of ParamAttr, conv3d_transpose
            will create ParamAttr as param_attr. If the Initializer of the param_attr
            is not set, the parameter is initialized with Xavier. The default value is None.
        bias_attr (ParamAttr|bool, optional): The parameter attribute for the bias of conv3d_transpose.
            If it is set to False, no bias will be added to the output units.
            If it is set to None or one attribute of ParamAttr, conv3d_transpose
            will create ParamAttr as bias_attr. If the Initializer of the bias_attr
            is not set, the bias is initialized zero. The default value is None.
        output_size(int|list|tuple, optional): The output image size. If output size is a
            tuple, it must contain two integers, (image_H, image_W). None if use
            filter_size, padding, and stride to calculate output_size.
            if output_size and filter_size are specified at the same time, They
            should follow the formula above. Default: None.
        data_format (str, optional): Data format that specifies the layout of input.
            It can be "NCDHW" or "NDHWC". Default: "NCDHW".

    Attribute:
        **weight** (Parameter): the learnable weights of filters of this layer.

        **bias** (Parameter): the learnable bias of this layer.

    Shape:
        - x: :math:`(N, C_{in}, D_{in}, H_{in}, W_{in})`

        - output: :math:`(N, C_{out}, D_{out}, H_{out}, W_{out})`

        Where

        .. math::

           D^\prime_{out} &= (D_{in} - 1) * strides[0] - 2 * paddings[0] + dilations[0] * (kernel_size[0] - 1) + 1 \\\\
           H^\prime_{out} &= (H_{in} - 1) * strides[1] - 2 * paddings[1] + dilations[1] * (kernel_size[1] - 1) + 1 \\\\
           W^\prime_{out} &= (W_{in} - 1) * strides[2] - 2 * paddings[2] + dilations[2] * (kernel_size[2] - 1) + 1 \\\\


    Raises:
        ValueError: If the shapes of input, filter_size, stride, padding and
                    groups mismatch.

    Examples:
       .. code-block:: python

          import numpy as np
          import paddle
          import paddle.nn as nn

          x = np.random.uniform(-1, 1, (2, 4, 8, 8, 8)).astype('float32')
          
          paddle.disable_static()

          x_var = paddle.to_tensor(x)
          conv = nn.Conv3DTranspose(4, 6, (3, 3, 3))
          y_var = conv(x_var)
          y_np = y_var.numpy()
          print(y_np.shape)
          
          # (2, 6, 10, 10, 10)
    """

    def __init__(self,
                 in_channels,
                 out_channels,
                 kernel_size,
                 stride=1,
                 padding=0,
                 output_padding=0,
                 dilation=1,
                 groups=1,
                 weight_attr=None,
                 bias_attr=None,
                 data_format="NCDHW"):
        super(ConvTranspose3d, self).__init__(
            in_channels,
            out_channels,
            kernel_size,
            True,
            3,
            stride=stride,
            padding=padding,
            dilation=dilation,
            output_padding=output_padding,
            groups=groups,
            weight_attr=weight_attr,
            bias_attr=bias_attr,
            data_format=data_format)

    def forward(self, x, output_size):
        if output_size is None:
            output_padding = self.output_padding
        else:
            output_padding = 0

        out = F.conv_transpose3d(
            x,
            self.weight,
            bias=self.bias,
            padding=self._padding,
            output_padding=output_padding,
            stride=self._stride,
            dilation=self._dilation,
            groups=self._groups,
            output_size=output_size,
            data_format=self._data_format)
        return out